Word for a person that is both caring and cold-hearted logical

I have an acquaintance who is a very cold, logical sort of person. She likes to make the 'best decision' for any situation, and wouldn't hesitate in a "kill one to save ten" sort of scenario. She doesn't celebrate any holidays (including her birthday) as she sees no good reason to. I could easily see her as a comic book villain, but at the same time, she's one of the most caring people I know. The past week she would gladly wish people a "Merry Christmas" or "Happy Hanukkah." If she hears you're sick, she'll make you homemade soup.

Perhaps the best way to describe her would be as a caring machine. If you were sick, she'd care for you better than anyone else, but wouldn't hesitate to euthanize you if the situation called for it, nor would she shed a tear.

I've been struggling to come up with a word for her, and simply calling her logical or "a machine with a heart" seems inappropriate. Is there a word for a person that is both very caring, but will not hesitate to be cold and logical when necessary? I know this is the English language stackexchange, but I'd settle for a word in another language if there's no English equivalent.

I think you're describing someone who is selfless (in a healthy way), in that she really does seek the good of others, but also very rational/logical. I'm not sure there is a word that combines these two different aspects of personality.

Maybe the most encompassing word is a plain one: thoughtful, because it has two fitting definitions:

1. given to careful thought; exhibiting or characterized by careful thought: a thoughtful essay 2. having or showing heed for the well-being or happiness of others and a propensity for anticipating their needs or wishes.

You can call her judicious (having, exercising, or characterized by good judgment; discreet, prudent, balanced, or wise) or circumspect (heedful of circumstances and potential consequences; prudent). But it doesn't quite capture her kindness as does thoughtful.

You may be looking for

affectless adj
Having or showing no emotion; unfeeling

[See TheFreeDictionary]

You could use the word "pragmatic", in the sense that your friend does the logical thing without consideration for its implications - good or bad.

That sounds like a typical description of judges.

The nearest single-word adjective might be "just", which has connotations of both "empathy / fairness", yet "logic taken to an extreme".

Otherwise, you might want to consider using a phrase instead of a single word, e.g. "impartial/rational, yet/and empathetic/caring".

utilitarian
The word utilitarian was coined by the philosopher and judge Jeremy Bentham, who argued that his principle of utility would create the "greatest happiness for the greatest number of people." The noun form of utilitarian refers to a person who adheres to this philosophy of usefulness.
https://www.vocabulary.com/dictionary/utilitarian

In other words, the person in question gauges their ethical and moral choices based on the perceived total value to all affected. The low utility cost of making soup is greatly outweighed by the benefit of making someone feel better, so it is not even a question, it is clearly the right choice.

A non-utilitarian might simply be too busy, or they might be worried their soup won't taste good, or they assume someone else will do it. These things just don't matter to a utilitarian, it's simply [value gained] - [value lost] = [positive].

Conversely, many people, when seeing a loved one suffer, would gladly take the suffering upon themselves, if possible, to spare the other. This might even be seen as selfless and heroic, but to a utilitarian it is nonsensical as the net outcome would be 0.

In these terms, it is easy to see the rationale behind killing 1 to save 10. Most people would rather "allow" 10 people to die through non-action than actively murder 1 person, but to a utilitarian, 1 life lost is objectively better than 10 lives lost, end of story.

In the end, it has nothing to do with them not caring, or having no emotions or even being "cold". They simply value the greater good above all else.